Question: Simplify the following expression: $ p = \dfrac{6r}{r - 3} + \dfrac{1}{8} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{6r}{r - 3} \times \dfrac{8}{8} = \dfrac{48r}{8r - 24} $ Multiply the second expression by $\dfrac{r - 3}{r - 3}$ $ \dfrac{1}{8} \times \dfrac{r - 3}{r - 3} = \dfrac{r - 3}{8r - 24} $ Therefore $ p = \dfrac{48r}{8r - 24} + \dfrac{r - 3}{8r - 24} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{48r + r - 3}{8r - 24} $ $p = \dfrac{49r - 3}{8r - 24}$